Multiplication principle - practice problems
The Multiplication Principle (also called the Fundamental Counting Principle or Rule of Product) is a fundamental concept in combinatorics that allows us to determine the total number of possible outcomes when performing a sequence of independent events or choices.Definition:
If:
- There are n ways to perform the first action,
- And for each of these, there are m ways to perform a second action (independent of the first),
then the total number of ways to perform both actions in sequence is:
n × m
Also is valid Generalized rule for Multiple Actions. The choices must be independent (the selection of one option does not affect the others).
Number of problems found: 579
- Pair of dice
In a throw of a pair of dice, find the probability of the same number on each die. - A restaurant’s
A restaurant’s menu has 3 appetizers, 3 mains and 2 desserts. In how many way can a 3-course meal be ordered? - Divisors 7
If 540=2²×3³×5, what is the number of all factors of 540? - Diagonals
What is the number of diagonals of a decagon? - The marathon
Twelve athletes are joining the Topolcany Marathon Event. How many ways can the first, second, and third placers be chosen? - Richard Richard is conducting an experiment. Every time he flips a fair two-sided coin, he also rolls a six-sided die. What is the probability that the coin will land on tails and the die will land on an even number?
- Locker combination
Todd forgot the first two numbers of his locker combination. The numbers can be any number 1 through 6. What is the probability that he will guess the first number correctly and the second number incorrectly?
- Five couples
In how many ways can 5 couples arrange themselves in a row if they stay together? - A bag 6
A bag contains 3 red marbles, 8 blue marbles, and 5 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 1000th, that both marbles drawn will be blue? - An ice cream
An ice cream machine has 3 flavors - vanilla, chocolate, and strawberry. The ice cream can be served in 2 ways - in a cone or in a cup. Along with the ice cream, there are 5 options for toppings - hot fudge, caramel, nuts, cherries, and sprinkles. What is - TF quiz
Gomer has to take a 5 question true/false quiz, but he hasn't studied. He will guess at each problem. In how many different ways is it possible to answer the quiz questions? How likely is it that he will get a score of 100%? - And or logic
If A and B are events with P(A)=0.3, P(A OR B)=0.76, and P(A AND B)=0.04, find P(B). Enter your answer in decimal form, rounded to one place. - A basket 4
A basket contains 9 fruits, where 4 are oranges, and the rest are mangoes. Three fruits are taken out one at a time and put aside. Find the probability that 3 are oranges. - A ferry
A ferry with a capacity of 10 people takes a group of 13 men and 7 women across a river. Find the number of ways in which the group may be taken across the if all women go on the first group. - Two dice 3 Two dice are thrown together. What is the probability that the number obtained on one of the dice is a multiple of the number obtained on the other dice? 2/3 9/36 12/36 11/18
- Student examination
How many ways can a teacher select a group of 6 students to sit in the front row if the class has 13 students? - 52 cards
A hand of five cards is dealt from a pack of 52 playing cards. How many different hands can be dealt that contain three aces? - A fair dice
A fair six-sided dice are rolled. What is the probability that the first number rolled is greater than 1 and the second number rolled is odd? Type your answer as a fraction in the simplest form. - A fair 2 A fair die is thrown two times. What is the probability that the sum of the score is almost 8?
- The probability 2 The probability that an adult possesses a credit card is 0.71. A researcher selects two adults at random. The probability (rounded to three decimal places) that the first adult possesses a credit card and the second adult does not possess a credit card is
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